In recent years, a new theory of the evolution of microbes under normal and stressed conditions has emerged, mainly in reference with the development of fractals and of self-organized mapping (SOM) concepts. This theory has much improved our understanding of the growth pattern of microbes like bacteria which determine their dynamics of evolution. In the first part of this paper, the main ideas in the theory of microbial self-organization are outlined, and some remarkable features of the resulting growth patterns are presented. In the second part, we apply conceptual tools developed in the context of fractal geometry to the study of the scaling properties of the bacterial growth in context with SOM patterns. We observe that such growth patterns appear to be more complex than simple fractals, although in some cases a simple fractal framework may be adequate for their description. © 2018, Springer Nature Singapore Pte Ltd.